If this is going to be a Police/Military shotgun, or a gun you're going to bet your life on, probably the last thing you really need is a more complicated trigger assembly.

Simple is better, because the more complicated something is, the more likely it is to fail when most needed.
Adjustable triggers in any firearm are well known to lose adjustment when least expected and most needed.
This can range from the trigger suddenly and disconcertingly becoming terrible, to a trigger that simply fails to fire the gun.

The stock Remington factory trigger unit is fairly simple and has a 50 year reputation of not giving problems.
For the shooting you've described, a fine adjustable trigger is very much over-kill and an added risk you don't have to take.
You don't need a fine trigger to blow a lock off at zero feet, or to hit a target at 40 yards with a load of buckshot.
Any Remington 870 I've ever seen can put all slugs into a saucer at 50 yards with the stock trigger.